Integrating a product of linear forms over the unit simplex can be done in polynomial time if the number of variables n is fixed (V. Baldoni et al., 2011). In this note, we highlight that this problem is equivalent to obtaining the normalizing constant of state probabilities for a popular class of Markov processes used in queueing network theory. In light of this equivalence, we survey existing computational algorithms developed in queueing theory that can be used for exact integration. For example, under some regularity conditions, queueing theory algorithms can exactly integrate a product of linear forms of total degree N by solving N systems of linear equations.
翻译:将线性形式产品并入单单元简单x上,如果变量n的数量固定下来,可以在多元时间进行(V.Baldoni等人,2011年)。在本说明中,我们强调,这一问题相当于在排队网络理论中使用的流行类Markov过程的正常状态概率常数。鉴于这一等值,我们调查在排队理论中开发的可用于精确集成的现有计算算法。例如,在某些常规条件下,排队理论算法可以通过解决N线性方程系统,将全N线性形式的产品完全融合在一起。</s>